Question:
Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.
Correct Answer
$10830
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 10%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% per annum.
Method (1) Using Formula
Calculation of Simple Interest
Formula to Calculate Simple Interest
Simple Interest (SI) = Principal × Rate × Time
Thus, Simple Interest (SI) = $5700 × 10% × 9
= $5700 ×10/100 × 9
= 5700 × 10 × 9/100
= 57000 × 9/100
= 513000/100
= $5130
Thus, Simple Interest = $5130
Calculation of Amount
The total money paid to the lender by a borrower is called the Amount.
In other words, sum of priciple and interest is called the Amount.
Formula to Calculate the Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $5130
= $10830
Thus, Amount to be paid = $10830 Answer
Method (2)
Calculation of Amount when Principal, Rate of Simple Interest and Time are given
Calculation of Amount directly using Principal, SI, and Time
Formula to calculate the Amount
Amount (A) = Principal (P) + Principal(P) × Rate of Interest (SI) × Time (t)
⇒ A = P + PRT
Here in the question, P = $5700
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 9 years
Thus, Amount (A)
= $5700 + ($5700 × 10% × 9)
= $5700 + ($5700 ×10/100 × 9)
= $5700 + (5700 × 10 × 9/100)
= $5700 + (57000 × 9/100)
= $5700 + (513000/100)
= $5700 + $5130 = $10830
Thus, Amount (A) to be paid = $10830 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5700, the simple interest in 1 year
= 10/100 × 5700
= 10 × 5700/100
= 57000/100 = $570
Thus, simple interest for 1 year = $570
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $570 × 9 = $5130
Thus, Simple Interest (SI) = $5130
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $5130
= $10830
Thus, Amount to be paid = $10830 Answer
Similar Questions
(1) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $8642 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 6% simple interest?
(3) How much loan did Laura borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9812.5 to clear it?
(4) Calculate the amount due if Christopher borrowed a sum of $4000 at 10% simple interest for 4 years.
(5) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9112 to clear the loan, then find the time period of the loan.
(6) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6562.5 to clear it?
(7) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 4% simple interest.
(8) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 7% simple interest?
(9) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9460 to clear the loan, then find the time period of the loan.
(10) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 6% simple interest?